Floer homology and non-fibered knot detection

John A. Baldwin; Steven Sivek

doi:10.1017/fmp.2024.28

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arXiv · 2208.03307

Floer homology and non-fibered knot detection

John A. Baldwin·Steven Sivek

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Abstract

We prove for the first time that knot Floer homology and Khovanov homology can detect non-fibered knots, and that HOMFLY homology detects infinitely many such knots; these theories were previously known to detect a mere six knots, all fibered. These results rely on our main technical theorem, which gives a complete classification of genus-1 knots in the 3-sphere whose knot Floer homology in the top Alexander grading is 2-dimensional. We discuss applications of this classification to problems in Dehn surgery which are carried out in two sequels. These include a proof that $0$-surgery characterizes infinitely many knots, generalizing results of Gabai from his 1987 resolution of the Property R Conjecture.

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John A. Baldwin, Steven Sivek. 2022-08-05. Floer homology and non-fibered knot detection. https://doi.org/10.1017/fmp.2024.28

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